Frank Spitzer
   HOME
*





Frank Spitzer
Frank Ludvig Spitzer (July 24, 1926 – February 1, 1992) was an Austrian-born American mathematician who made fundamental contributions to probability theory, including the theory of random walks, fluctuation theory, percolation theory, the Wiener sausage, and especially the theory of interacting particle systems. Rare among mathematicians, he chose to focus broadly on " phenomena", rather than any one of the many specific theorems that might help to articulate a given phenomenon. His book ''Principles of Random Walk'', first published in 1964, remains a well-cited classic. Spitzer was born into a Jewish family in Vienna, Austria, and by the time he was twelve years old, the Nazi threat in Austria was evident. His parents were able to send him to a summer camp for Jewish children in Sweden, and, as a result, Spitzer spent all of the war years in Sweden. He lived with two Swedish families, learned Swedish, graduated from high school, and for one year attended Tekniska Hogskol ...
[...More Info...]      
[...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]  


picture info

Vienna
en, Viennese , iso_code = AT-9 , registration_plate = W , postal_code_type = Postal code , postal_code = , timezone = CET , utc_offset = +1 , timezone_DST = CEST , utc_offset_DST = +2 , blank_name = Vehicle registration , blank_info = W , blank1_name = GDP , blank1_info = € 96.5 billion (2020) , blank2_name = GDP per capita , blank2_info = € 50,400 (2020) , blank_name_sec1 = HDI (2019) , blank_info_sec1 = 0.947 · 1st of 9 , blank3_name = Seats in the Federal Council , blank3_info = , blank_name_sec2 = GeoTLD , blank_info_sec2 = .wien , website = , footnotes = , image_blank_emblem = Wien logo.svg , blank_emblem_size = Vienna ( ; german: Wien ; ba ...
[...More Info...]      
[...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]  


Interacting Particle System
In probability theory, an interacting particle system (IPS) is a stochastic process (X(t))_ on some configuration space \Omega= S^G given by a site space, a countable-infinite graph G and a local state space, a compact metric space S . More precisely IPS are continuous-time Markov jump processes describing the collective behavior of stochastically interacting components. IPS are the continuous-time analogue of stochastic cellular automata. Among the main examples are the voter model, the contact process, the asymmetric simple exclusion process (ASEP), the Glauber dynamics and in particular the stochastic Ising model. IPS are usually defined via their Markov generator giving rise to a unique Markov process using Markov semigroups and the Hille-Yosida theorem. The generator again is given via so-called transition rates c_\Lambda(\eta,\xi)>0 where \Lambda\subset G is a finite set of sites and \eta,\xi\in\Omega with \eta_i=\xi_i for all i\notin\Lambda. The rates describe ex ...
[...More Info...]      
[...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]  


picture info

Armed Forces
A military, also known collectively as armed forces, is a heavily armed, highly organized force primarily intended for warfare. It is typically authorized and maintained by a sovereign state, with its members identifiable by their distinct military uniform. It may consist of one or more military branches such as an army, navy, air force, space force, marines, or coast guard. The main task of the military is usually defined as defence of the state and its interests against external armed threats. In broad usage, the terms ''armed forces'' and ''military'' are often treated as synonymous, although in technical usage a distinction is sometimes made in which a country's armed forces may include both its military and other paramilitary forces. There are various forms of irregular military forces, not belonging to a recognized state; though they share many attributes with regular military forces, they are less often referred to as simply ''military''. A nation's military may ...
[...More Info...]      
[...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]  


picture info

Europe
Europe is a large peninsula conventionally considered a continent in its own right because of its great physical size and the weight of its history and traditions. Europe is also considered a Continent#Subcontinents, subcontinent of Eurasia and it is located entirely in the Northern Hemisphere and mostly in the Eastern Hemisphere. Comprising the westernmost peninsulas of Eurasia, it shares the continental landmass of Afro-Eurasia with both Africa and Asia. It is bordered by the Arctic Ocean to the north, the Atlantic Ocean to the west, the Mediterranean Sea to the south and Asia to the east. Europe is commonly considered to be Boundaries between the continents of Earth#Asia and Europe, separated from Asia by the drainage divide, watershed of the Ural Mountains, the Ural (river), Ural River, the Caspian Sea, the Greater Caucasus, the Black Sea and the waterways of the Turkish Straits. "Europe" (pp. 68–69); "Asia" (pp. 90–91): "A commonly accepted division between Asia and E ...
[...More Info...]      
[...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]  


picture info

North Africa
North Africa, or Northern Africa is a region encompassing the northern portion of the African continent. There is no singularly accepted scope for the region, and it is sometimes defined as stretching from the Atlantic shores of Mauritania in the west, to Egypt's Suez Canal. Varying sources limit it to the countries of Algeria, Libya, Morocco, and Tunisia, a region that was known by the French during colonial times as "''Afrique du Nord''" and is known by Arabs as the Maghreb ("West", ''The western part of Arab World''). The United Nations definition includes Morocco, Algeria, Tunisia, Libya, Egypt, Sudan, and the Western Sahara, the territory disputed between Morocco and the Sahrawi Republic. The African Union definition includes the Western Sahara and Mauritania but not Sudan. When used in the term Middle East and North Africa (MENA), it often refers only to the countries of the Maghreb. North Africa includes the Spanish cities of Ceuta and Melilla, and plazas de s ...
[...More Info...]      
[...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]  


picture info

France
France (), officially the French Republic ( ), is a country primarily located in Western Europe. It also comprises of Overseas France, overseas regions and territories in the Americas and the Atlantic Ocean, Atlantic, Pacific Ocean, Pacific and Indian Oceans. Its Metropolitan France, metropolitan area extends from the Rhine to the Atlantic Ocean and from the Mediterranean Sea to the English Channel and the North Sea; overseas territories include French Guiana in South America, Saint Pierre and Miquelon in the North Atlantic, the French West Indies, and many islands in Oceania and the Indian Ocean. Due to its several coastal territories, France has the largest exclusive economic zone in the world. France borders Belgium, Luxembourg, Germany, Switzerland, Monaco, Italy, Andorra, and Spain in continental Europe, as well as the Kingdom of the Netherlands, Netherlands, Suriname, and Brazil in the Americas via its overseas territories in French Guiana and Saint Martin (island), ...
[...More Info...]      
[...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]  


picture info

Stockholm
Stockholm () is the Capital city, capital and List of urban areas in Sweden by population, largest city of Sweden as well as the List of urban areas in the Nordic countries, largest urban area in Scandinavia. Approximately 980,000 people live in the Stockholm Municipality, municipality, with 1.6 million in the Stockholm urban area, urban area, and 2.4 million in the Metropolitan Stockholm, metropolitan area. The city stretches across fourteen islands where Mälaren, Lake Mälaren flows into the Baltic Sea. Outside the city to the east, and along the coast, is the island chain of the Stockholm archipelago. The area has been settled since the Stone Age, in the 6th millennium BC, and was founded as a city in 1252 by Swedish statesman Birger Jarl. It is also the county seat of Stockholm County. For several hundred years, Stockholm was the capital of Finland as well (), which then was a part of Sweden. The population of the municipality of Stockholm is expected to reach o ...
[...More Info...]      
[...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]  


picture info

Royal Institute Of Technology
The KTH Royal Institute of Technology ( sv, Kungliga Tekniska högskolan, lit=Royal Institute of Technology), abbreviated KTH, is a public research university in Stockholm, Sweden. KTH conducts research and education in engineering and technology and is Sweden's largest technical university. Currently, KTH consists of five schools with four campuses in and around Stockholm. KTH was established in 1827 as the ''Teknologiska institutet (Institute of Technology)'' and had its roots in the ''Mekaniska skolan (School of Mechanics)'' that was established in 1798 in Stockholm. But the origin of KTH dates back to the predecessor of the ''Mekaniska skolan'', the ''Laboratorium mechanicum'', which was established in 1697 by the Swedish scientist and innovator Christopher Polhem. The Laboratorium mechanicum combined education technology, a laboratory, and an exhibition space for innovations. In 1877 KTH received its current name, Kungliga Tekniska högskolan (KTH Royal Institute of Technol ...
[...More Info...]      
[...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]  


picture info

Swedish Language
Swedish ( ) is a North Germanic language spoken predominantly in Sweden and in parts of Finland. It has at least 10 million native speakers, the fourth most spoken Germanic language and the first among any other of its type in the Nordic countries overall. Swedish, like the other Nordic languages, is a descendant of Old Norse, the common language of the Germanic peoples living in Scandinavia during the Viking Era. It is largely mutually intelligible with Norwegian and Danish, although the degree of mutual intelligibility is largely dependent on the dialect and accent of the speaker. Written Norwegian and Danish are usually more easily understood by Swedish speakers than the spoken languages, due to the differences in tone, accent, and intonation. Standard Swedish, spoken by most Swedes, is the national language that evolved from the Central Swedish dialects in the 19th century and was well established by the beginning of the 20th century. While distinct regional varieties ...
[...More Info...]      
[...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]  


Sweden
Sweden, formally the Kingdom of Sweden,The United Nations Group of Experts on Geographical Names states that the country's formal name is the Kingdom of SwedenUNGEGN World Geographical Names, Sweden./ref> is a Nordic country located on the Scandinavian Peninsula in Northern Europe. It borders Norway to the west and north, Finland to the east, and is connected to Denmark in the southwest by a bridgetunnel across the Öresund. At , Sweden is the largest Nordic country, the third-largest country in the European Union, and the fifth-largest country in Europe. The capital and largest city is Stockholm. Sweden has a total population of 10.5 million, and a low population density of , with around 87% of Swedes residing in urban areas in the central and southern half of the country. Sweden has a nature dominated by forests and a large amount of lakes, including some of the largest in Europe. Many long rivers run from the Scandes range through the landscape, primarily ...
[...More Info...]      
[...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]  


picture info

Summer Camp
A summer camp or sleepaway camp is a supervised program for children conducted during the summer months in some countries. Children and adolescents who attend summer camp are known as ''campers''. Summer school is usually a part of the academic curriculum for a student to make up work not accomplished during the academic year (summer camps can include academic work, but is not a requirement for graduation). The traditional view of a summer camp as a woody place with hiking, canoeing, and campfires is changing, with greater acceptance of newer types of summer camps that offer a wide variety of specialized activities. For example, there are camps for the performing arts, music, magic, computer programming, language learning, mathematics, children with special needs, and weight loss. In 2006, the American Camp Association reported that 75 percent of camps added new programs. This is largely to counter a trend in decreasing enrollment in summer camps, which some argue to have bee ...
[...More Info...]      
[...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]  


picture info

Nazism
Nazism ( ; german: Nazismus), the common name in English for National Socialism (german: Nationalsozialismus, ), is the far-right totalitarian political ideology and practices associated with Adolf Hitler and the Nazi Party (NSDAP) in Nazi Germany. During Hitler's rise to power in 1930s Europe, it was frequently referred to as Hitlerism (german: Hitlerfaschismus). The later related term "neo-Nazism" is applied to other far-right groups with similar ideas which formed after the Second World War. Nazism is a form of fascism, with disdain for liberal democracy and the parliamentary system. It incorporates a dictatorship, fervent antisemitism, anti-communism, scientific racism, and the use of eugenics into its creed. Its extreme nationalism originated in pan-Germanism and the ethno-nationalist '' Völkisch'' movement which had been a prominent aspect of German nationalism since the late 19th century, and it was strongly influenced by the paramilitary groups that emerged af ...
[...More Info...]      
[...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]