Frank Spitzer
Encyclopedia
Frank Ludvig Spitzer was an Austrian
-born American
mathematician
who made fundamental contributions to probability theory
, including the theory of random walk
s, 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 theorem
s that might help to articulate a given phenomenon. His book "Principles of Random Walks", 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 Hogskolan
in Stockholm
.
During the war years, Spitzer's parents and his sister were able to make their way to the United States
by passing through the unoccupied parts of France
and North Africa
, and, after the war, Spitzer joined his family in their new country. Spitzer enlisted in the U.S. Army just as the war in Europe
was ending. After completing his military service
in 1947, Spitzer entered the University of Michigan
(Ann Arbor) to study mathematics. His studies went quickly, and he completed his B.A. and Ph.D. in just six years.
Spitzer's first academic appointments were at the California Institute of Technology
(1953–1958), but most of his academic career was spent at Cornell University
, with leaves at the Institute for Advanced Study in Princeton
and the Mittag-Leffler Institute in Sweden. Among many his many honors, Spitzer was a member of the National Academy of Sciences
.
Austrians
Austrians are a nation and ethnic group, consisting of the population of the Republic of Austria and its historical predecessor states who share a common Austrian culture and Austrian descent....
-born American
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
who made fundamental contributions to probability theory
Probability theory
Probability theory is the branch of mathematics concerned with analysis of random phenomena. The central objects of probability theory are random variables, stochastic processes, and events: mathematical abstractions of non-deterministic events or measured quantities that may either be single...
, including the theory of random walk
Random walk
A random walk, sometimes denoted RW, is a mathematical formalisation of a trajectory that consists of taking successive random steps. For example, the path traced by a molecule as it travels in a liquid or a gas, the search path of a foraging animal, the price of a fluctuating stock and the...
s, fluctuation theory, percolation theory
Percolation theory
In mathematics, percolation theory describes the behavior of connected clusters in a random graph. The applications of percolation theory to materials science and other domains are discussed in the article percolation.-Introduction:...
, the Wiener sausage
Wiener sausage
In the mathematical field of probability, the Wiener sausage is a neighborhood of the trace of a Brownian motion up to a time t, given by taking all points within a fixed distance of Brownian motion. It can be visualized as a sausage of fixed radius whose centerline is Brownian motion...
, and especially the theory
Theory
The English word theory was derived from a technical term in Ancient Greek philosophy. The word theoria, , meant "a looking at, viewing, beholding", and referring to contemplation or speculation, as opposed to action...
of interacting particle systems
Particle Systems
Particle Systems Ltd. was a computer game developer based in Sheffield, England. The company was founded by Glyn Williams and Michael Powell. Games developed by Particle Systems include Independence War and its sequel Independence War 2: Edge of Chaos...
. Rare among mathematicians, he chose to focus broadly on "phenomena
Phenomenon
A phenomenon , plural phenomena, is any observable occurrence. Phenomena are often, but not always, understood as 'appearances' or 'experiences'...
", rather than any one of the many specific theorem
Theorem
In mathematics, a theorem is a statement that has been proven on the basis of previously established statements, such as other theorems, and previously accepted statements, such as axioms...
s that might help to articulate a given phenomenon. His book "Principles of Random Walks", first published in 1964, remains a well-cited classic.
Spitzer was born into a Jewish family in Vienna
Vienna
Vienna is the capital and largest city of the Republic of Austria and one of the nine states of Austria. Vienna is Austria's primary city, with a population of about 1.723 million , and is by far the largest city in Austria, as well as its cultural, economic, and political centre...
, Austria
Austria
Austria , officially the Republic of Austria , is a landlocked country of roughly 8.4 million people in Central Europe. It is bordered by the Czech Republic and Germany to the north, Slovakia and Hungary to the east, Slovenia and Italy to the south, and Switzerland and Liechtenstein to the...
, and by the time he was twelve years old, the Nazi
Nazism
Nazism, the common short form name of National Socialism was the ideology and practice of the Nazi Party and of Nazi Germany...
threat in Austria was evident. His parents were able to send him to a summer camp
Summer camp
Summer camp is a supervised program for children or teenagers conducted during the summer months in some countries. Children and adolescents who attend summer camp are known as campers....
for Jewish children in Sweden
Sweden
Sweden , officially the Kingdom of Sweden , is a Nordic country on the Scandinavian Peninsula in Northern Europe. Sweden borders with Norway and Finland and is connected to Denmark by a bridge-tunnel across the Öresund....
, and, as a result, Spitzer spent all of the war years in Sweden. He lived with two Swedish families, learned Swedish
Swedish language
Swedish is a North Germanic language, spoken by approximately 10 million people, predominantly in Sweden and parts of Finland, especially along its coast and on the Åland islands. It is largely mutually intelligible with Norwegian and Danish...
, graduated from high school, and for one year attended Tekniska Hogskolan
Royal Institute of Technology
The Royal Institute of Technology is a university in Stockholm, Sweden. KTH was founded in 1827 as Sweden's first polytechnic and is one of Scandinavia's largest institutions of higher education in technology. KTH accounts for one-third of Sweden’s technical research and engineering education...
in Stockholm
Stockholm
Stockholm is the capital and the largest city of Sweden and constitutes the most populated urban area in Scandinavia. Stockholm is the most populous city in Sweden, with a population of 851,155 in the municipality , 1.37 million in the urban area , and around 2.1 million in the metropolitan area...
.
During the war years, Spitzer's parents and his sister were able to make their way to the United States
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
by passing through the unoccupied parts of France
France
The French Republic , The French Republic , The French Republic , (commonly known as France , is a unitary semi-presidential republic in Western Europe with several overseas territories and islands located on other continents and in the Indian, Pacific, and Atlantic oceans. Metropolitan France...
and North Africa
North Africa
North Africa or Northern Africa is the northernmost region of the African continent, linked by the Sahara to Sub-Saharan Africa. Geopolitically, the United Nations definition of Northern Africa includes eight countries or territories; Algeria, Egypt, Libya, Morocco, South Sudan, Sudan, Tunisia, and...
, and, after the war, Spitzer joined his family in their new country. Spitzer enlisted in the U.S. Army just as the war in Europe
Europe
Europe is, by convention, one of the world's seven continents. Comprising the westernmost peninsula of Eurasia, Europe is generally 'divided' from Asia to its east by the watershed divides of the Ural and Caucasus Mountains, the Ural River, the Caspian and Black Seas, and the waterways connecting...
was ending. After completing his military service
Armed forces
The armed forces of a country are its government-sponsored defense, fighting forces, and organizations. They exist to further the foreign and domestic policies of their governing body, and to defend that body and the nation it represents from external aggressors. In some countries paramilitary...
in 1947, Spitzer entered the University of Michigan
University of Michigan
The University of Michigan is a public research university located in Ann Arbor, Michigan in the United States. It is the state's oldest university and the flagship campus of the University of Michigan...
(Ann Arbor) to study mathematics. His studies went quickly, and he completed his B.A. and Ph.D. in just six years.
Spitzer's first academic appointments were at the California Institute of Technology
California Institute of Technology
The California Institute of Technology is a private research university located in Pasadena, California, United States. Caltech has six academic divisions with strong emphases on science and engineering...
(1953–1958), but most of his academic career was spent at Cornell University
Cornell University
Cornell University is an Ivy League university located in Ithaca, New York, United States. It is a private land-grant university, receiving annual funding from the State of New York for certain educational missions...
, with leaves at the Institute for Advanced Study in Princeton
Princeton, New Jersey
Princeton is a community located in Mercer County, New Jersey, United States. It is best known as the location of Princeton University, which has been sited in the community since 1756...
and the Mittag-Leffler Institute in Sweden. Among many his many honors, Spitzer was a member of the National Academy of Sciences
United States National Academy of Sciences
The National Academy of Sciences is a corporation in the United States whose members serve pro bono as "advisers to the nation on science, engineering, and medicine." As a national academy, new members of the organization are elected annually by current members, based on their distinguished and...
.
External links
- Biographical memoir – by Harry KestenHarry KestenHarry Kesten is an American mathematician best known for his work in probability, most notably on random walks and percolation theory.- Biography :...